The "sakabatou", or "reverse-bladed katana", is a fictional weapon invented by Watsuki Nobuhiro for his comic, Rurouni Kenshin. It's one of the truly unique elements of Kenshin which helped it to stand out from the dozens of similar samurai manga. After all, the idea of a violent-pacifistic group of justice-seekers wandering pre-Meiji Japan is about as old as samurai dramas are.
Fundamentally, the sakabatou is a rather absurd idea -- getting hit in the head or neck by the blunt side of a 1.5kg sword is almost as likely to be deadly as being cut by it. In the manga, we find that with this weapon, the protagonist, Himura Kenshin, has the fantastic skill to disarm, incapacitate, and occasionally maim his opponents without causing fatal injury. In this, his sword symbolizes Kenshin's reversal from killer to pacifist.
Kenshin also has incredible control wielding the blade backwards to bring the sharp side to bear. Uncountable inanimate objects suffer the wrath of this potentially lethal slice -- in one scene, we even see Kenshin cleave a flying cannon-ball in half. We realize that Kenshin could use the sword thusly to kill -- as he tries to do to Udou Jin'ei towards the beginning of the story. The hidden, sharp edge shows Kenshin's dark side, and the very real threat that he could kill again provides the tension to develop him as a round character.
In the animated Rurouni Kenshin TV show, one episode finds Kenshin drawn into a fight against Saitou Hajime. Again, he is faced with the pacifist's paradox of "kill an evil man or allow an innocent to be killed". Much as the sword wants to turn itself around, revealing its lethal edge, Kenshin finds himself drawn deeper and deeper to the fight. Kenshin's struggle not only against his enemy, but also against himself, is what makes this scene memorable among the countless samurai vs. samurai duels of Japanese TV history.
Say all you want about the characters, plot, drama, and art. These were all necessary for competing in the mass-market manga world, but the sakaba sword instantly symbolizes what made Kenshin special.
In the book, sakabatou is written in kanji as: 逆刃刀 (backwards, blade, sword.) If you can't read these Unicode characters, see here.